Approximation Theorems of Mathematical Statistics

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners.

Author: Robert J. Serfling

Publisher: Wiley-Interscience

ISBN: 0471219274

Category: Mathematics

Page: 400

View: 754

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures

Approximation Theorems of Mathematical Statistics

This book covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized.

Author: Robert J. Serfling

Publisher: John Wiley & Sons

ISBN: 9780470317198

Category: Mathematics

Page: 392

View: 812

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures

Modern Concepts and Theorems of Mathematical Statistics

Miller, R. G. Jr. (1981), Simultaneous Statistical Inference, 2nd edn, Springer-Verlag, New York. Milton, J. S. and Tsokos, C. P. (1976), ... Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, Wiley, New York.

Author: Edward B. Manoukian

Publisher: Springer Science & Business Media

ISBN: 9781461248569

Category: Mathematics

Page: 156

View: 176

With the rapid progress and development of mathematical statistical methods, it is becoming more and more important for the student, the in structor, and the researcher in this field to have at their disposal a quick, comprehensive, and compact reference source on a very wide range of the field of modern mathematical statistics. This book is an attempt to fulfill this need and is encyclopedic in nature. It is a useful reference for almost every learner involved with mathematical statistics at any level, and may supple ment any textbook on the subject. As the primary audience of this book, we have in mind the beginning busy graduate student who finds it difficult to master basic modern concepts by an examination of a limited number of existing textbooks. To make the book more accessible to a wide range of readers I have kept the mathematical language at a level suitable for those who have had only an introductory undergraduate course on probability and statistics, and basic courses in calculus and linear algebra. No sacrifice, how ever, is made to dispense with rigor. In stating theorems I have not always done so under the weakest possible conditions. This allows the reader to readily verify if such conditions are indeed satisfied in most applications given in modern graduate courses without being lost in extra unnecessary mathematical intricacies. The book is not a mere dictionary of mathematical statistical terms.

Limit Theorems in Probability  Statistics and Number Theory

Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and ...

Author: Peter Eichelsbacher

Publisher: Springer Science & Business Media

ISBN: 9783642360688

Category: Mathematics

Page: 317

View: 353

​Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.

Probability Theory and Mathematical Statistics

The topics treated fall into three main groups, all of which deal with classical problems which originated in the work of Kolmogorov.

Author: Ibragimoc

Publisher: CRC Press

ISBN: 2919875140

Category: Mathematics

Page: 320

View: 637

The topics treated fall into three main groups, all of which deal with classical problems which originated in the work of Kolmogorov. The first section looks at probability limit theorems, the second deals with stochastic analysis, and the final part presents some papers on non-parametric and semi-parametric models of mathematical statistics and asymptotic problems. The contributions come from some of the foremost mathematicians in the world today, making for a truly international collection of papers, permeated with the influence of Kolmogorov's works.

Modern concepts and theorems of mathematical statistics

Author: Edward B. Manoukian

Publisher: Springer Verlag

ISBN: MINN:319510003176528

Category: Mathematics

Page: 156

View: 147

Mathematical Statistics

Sequential Nonparametrics: Invariance Principles and Statistical Inference. Wiley, New York. Sen, P. K. and Singer, J. M. (1993). Large Sample Methods in Statistics. Chapman & Hall, London. Serfling, R. J. (1980). Approximation Theorems ...

Author: Jun Shao

Publisher: Springer Science & Business Media

ISBN: 9780387217185

Category: Mathematics

Page: 592

View: 237

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. This new edition has been revised and updated and in this fourth printing, errors have been ironed out. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Subsequent chapters contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.

A Course in Mathematical Statistics and Large Sample Theory

Approximation theorems of mathematical statistics. New York: Wiley. Shevtsova, I. G. (2010). An improvement of convergence rate estimates in the Lyapunov theorem. Doklady Mathematics, 82(3), 862–864. Chapter 7 Large Sample Theory of ...

Author: Rabi Bhattacharya

Publisher: Springer

ISBN: 9781493940325

Category: Mathematics

Page: 389

View: 470

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

Strong Approximations in Probability and Statistics

This book will prove useful to mathematicians and advance mathematics students.

Author: M. Csörgo

Publisher: Academic Press

ISBN: 9781483268040

Category: Mathematics

Page: 286

View: 147

Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students.

Mathematical Statistics

Scandinavian Journal of Statistics, 9, 165–169. Sen, P. K. (1986). Are BAN estimators the Pitman-closest ones too? Sankhy ̄a Series A 48, 51–58. Serfling, R. J. (1980). Approximation theorems of mathematical statistics. New York: Wiley.

Author: Johann Pfanzagl

Publisher: Springer

ISBN: 9783642310843

Category: Mathematics

Page: 316

View: 733

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson's Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Mathematical Statistics for Economics and Business

We present some results for the asymptotic properties of the GLR test ahead. Additional results can be found in S. Wilks (1962), Mathematical Statistics. New York: John Wiley, p. 419, and R. J. Serfling (1980), Approximation Theorems of ...

Author: Ron C. Mittelhammer

Publisher: Springer Science & Business Media

ISBN: 9781461239888

Category: Mathematics

Page: 724

View: 340

A comprehensive introduction to the principles underlying statistical analyses in the fields of economics, business, and econometrics. The selection of topics is specifically designed to provide students with a substantial conceptual foundation, from which to achieve a thorough and mature understanding of statistical applications within the fields. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. Includes hundreds of exercises and problems.

Series Approximation Methods in Statistics

Mathews, J., and Walker, R.L. (1964), Mathematical Methods of Physics, New York: W.A. Benjamin, Inc.. ... Serfling, R.J. (1980), Approximation Theorems of Mathematical Statistics, New York: Wiley. Skates, S.J. (1993), "On Secant ...

Author: John E. Kolassa

Publisher: Springer Science & Business Media

ISBN: 9781475742756

Category: Mathematics

Page: 153

View: 657

This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.

Mathematical Statistics

SERFLING , R. J., Approximation Theorems of Mathematical Statistics New York: J. Wiley & Sons, 1980. STIGLER , S., The History of Statistics: The Measurement of Uncertainty Before 1900 Cambridge, MA: Harvard University Press, 1986.

Author: Peter .J. Bickel

Publisher: CRC Press

ISBN: 9781498740418

Category: Business & Economics

Page: 1021

View: 702

Volume I presents fundamental, classical statistical concepts at the doctorate level without using measure theory. It gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods. Volume II covers a number of topics that are important in current measure theory and practice. It emphasizes nonparametric methods which can really only be implemented with modern computing power on large and complex data sets. In addition, the set includes a large number of problems with more difficult ones appearing with hints and partial solutions for the instructor.

Probability Theory and Mathematical Statistics

Approximation Theorems of Mathematical Statistics . J. Wiley , New York . Serfling , R. ( 1984 ) . Generalized L- , M- and R - statistics . Ann . Statist . 12 , 76-86 . Schneemeier , W. ( 1985 ) . Unpublished Ph . D. Dissertation .

Author: Yu. V. Prohorov

Publisher: VSP

ISBN: 9067640670

Category: Mathematical statistics

Page: 574

View: 887

Probability Theory and Mathematical Statistics  Vol  1

U-processes ; rates of convergence. Technical report, Yale University. Serfling, R. (1980). Approximation Theorems of Mathematical Statistics. J. Wiley, New York. Serfling, R. (1981). Generalized L-, M- and R-statistics. Ann. Statist.

Author: Yu. V. Prohorov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783112319000

Category: Technology & Engineering

Page: 583

View: 846

Mathematical Statistics With Applications

Show using the central limit theorem that the probability distribution function of the quantity Xn−nn may be approximated by the standard normal distribution. 17. ... Approximation Theorems of Mathematical Statistics. New York.

Author: Asha Seth Kapadia

Publisher: CRC Press

ISBN: 9781351992046

Category: Mathematics

Page: 648

View: 404

Mathematical statistics typically represents one of the most difficult challenges in statistics, particularly for those with more applied, rather than mathematical, interests and backgrounds. Most textbooks on the subject provide little or no review of the advanced calculus topics upon which much of mathematical statistics relies and furthermore contain material that is wholly theoretical, thus presenting even greater challenges to those interested in applying advanced statistics to a specific area. Mathematical Statistics with Applications presents the background concepts and builds the technical sophistication needed to move on to more advanced studies in multivariate analysis, decision theory, stochastic processes, or computational statistics. Applications embedded within theoretical discussions clearly demonstrate the utility of the theory in a useful and relevant field of application and allow readers to avoid sudden exposure to purely theoretical materials. With its clear explanations and more than usual emphasis on applications and computation, this text reaches out to the many students and professionals more interested in the practical use of statistics to enrich their work in areas such as communications, computer science, economics, astronomy, and public health.

Mathematical Statistics

Serfling R. J., Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980. 108. Shiryaev A. N., Probability, Nauka, Moscow, 1980. (Russian) 109. Shorack G. R. and Wellner J. A., Empirical Processes with Applications to ...

Author: A A Borokov

Publisher: Routledge

ISBN: 9781351433105

Category: Mathematics

Page: 592

View: 343

A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. The author presents classical results and methods that form the basis of modern statistics, and examines the foundations o

Mathematical Statistics with Applications

Introduction to Mathematical Statistics, 6th ed. Upper Saddle River, N.J.: Pearson Prentice ... John E. Freund's Mathematical Statistics with Applications, 7th ed. ... Approximation Theorems of Mathematical Statistics. New York: Wiley.

Author: Dennis Wackerly

Publisher: Cengage Learning

ISBN: 9781111798789

Category: Mathematics

Page: 944

View: 432

In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps students discover the nature of statistics and understand its essential role in scientific research. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Probability Theory and Mathematical Statistics for Engineers

[26] Serfling, R.J., "Approximation Theorems in Mathematical Statistics', John Wiley & Sons, New York (1980). |27) Wadsworth, H.M. (editor), 'Handbook of Statistical Methods for Engineers and Scientists', McGraw-Hill, New York (1990).

Author: Paolo L. Gatti

Publisher: CRC Press

ISBN: 9781482267761

Category: Architecture

Page: 368

View: 962

Probability Theory and Statistical Methods for Engineers brings together probability theory with the more practical applications of statistics, bridging theory and practice. It gives a series of methods or recipes which can be applied to specific problems. This book is essential reading for practicing engineers who need a sound background knowledge of probabilistic and statistical concepts and methods of analysis for their everyday work. It is also a useful guide for graduate engineering students.

Mathematical Statistics and Applications

Approximation Theorems of Mathematical Statistics . John Wiley , New York . Simon , G. ( 1977 ) . A nonparametric test of total independence based on Kendall's tau . Biometrika , 64 , 277–282 . Stewart , D. and Love , W. ( 1968 ) .

Author: Constance van Eeden

Publisher: IMS

ISBN: 0940600579

Category: Mathematics

Page: 495

View: 927